Problem: What do the following two equations represent? $-x-4y = -4$ $x+4y = 3$
Answer: Putting the first equation in $y = mx + b$ form gives: $-x-4y = -4$ $-4y = x-4$ $y = -\dfrac{1}{4}x + 1$ Putting the second equation in $y = mx + b$ form gives: $x+4y = 3$ $4y = -x+3$ $y = -\dfrac{1}{4}x + \dfrac{3}{4}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.